Interatomic Bonding
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Transcript Interatomic Bonding
Interatomic Bonding
Bonding Forces and Energies
Equilibrium atomic spacing
Minimization of bonding energy
Embedded Atom Method (EAM)
Types of Bonding
Ionic
Covalent
Secondary
Metallic
Bonding Forces and
Energy
Interatomic Forces
attractive forces (Fa)
repulsive forces (Fr)
When the atoms reach a critical distance
(r0), the attractive and repulsive forces
cancel each other and the atoms are at
their equilibrium distance.
Bonding Forces and
Energy
Bonding Forces and
Energy
Sometimes it is easier to deal with
potential energies (E) rather than forces.
The relation of Energy to Force is as
follows: r
EN
FN dr
EA ER
Equilibrium is reached by minimizing EN
Bonding Forces and
Energy
Embedded Atom Method
Potentials also calculated through the
embedded atom method (EAM)
potentials are calculated as a sum of pairwise
(interactions between a pair of atoms)
contributions and a many body term.
E V (rij ) F ( i )
i, j
i (rij )
j
i
Embedded Atom Method
If a ternary system is being studied, EAM
potentials may be defined by considering
the three individual binary systems that
make up the ternary system.
As long as the interatomic interaction used
for each of the pure components is the same
in the description of the two binaries.
The volume term is calculated as the
embedding energy of a local electron
density.
Embedded Atom Method
Effective pairs
equivalent potentials where the various
contributions (pair and volume) are not the
same but add up to the same total energy for
all possible simulations.
Called the effective pair scheme, it is defined
as when the first derivative of the embedding
function is taken as zero.
Embedded Atom Method
Potentials converted to Effective pair
scheme:
F ( ) F ( ) F ( 0 )
eff
V ( R) V (r ) 2 ( R) F ( 0 )
eff
Transformation where mixed potentials
are originally derived:
V (r ) VAB (r ) A (r ) F ( 0 B ) B (r ) F ( 0 A )
eff
AB
EAM Potentials
Some examples of EAM functions for
various metals
Ag:
EAM Potentials
Al:
Au:
EAM Potentials
Veff for various pure elements:
Ionic Bonding
Most common bonding in metal-nonmetal
compounds.
Atoms give up/receive electrons from other
atoms in the compound to form stable
electron configurations
Because of net electrical charge in each ion,
they attract each other and bond via
coulombic forces.
Ionic Bonding
Attractive and repulsive energies are
functions of interatomic distance and may
be represented as follows:
A
EA
r
B
EB n
r
A and B are constants depending upon the
system. The value of n is usually taken as
12.
Ionic Bonding
Properties of ionic bonding
nondirectional: magnitude of bond is equal in
all directions around the ion.
High bonding energies (~600 - 1500 kJ/mol)
reflected in high melting temperatures
generally hard and brittle materials
most common bonding for ceramic materials
electrically and thermally insulative materials
Covalent Bonding
Stable configurations are obtained by the
sharing of valence electrons by 2 or more
atoms.
Typical in nonmetallic compounds (CH4, H20)
Number of possible bonds per atom is
determined by the number of valence
electrons in the following formula:
number of bonds = 8 - (valence electrons)
Bonds also are angle dependent
Covalent Bonding
Properties of covalent bonding
can be either very strong or very weak
bonds, depending upon the atoms involved in
the bond. This is also reflected in the melting
temperature of the compound
ex: diamond (strong bond) -- Tm> 3350°C
bismuth (weak bond) -- Tm ~ 270°C
most common form of bonding in polymers
Secondary Bonding
Van der Waals bonding
weak bonds in comparison with other forms
of bonding (~10 kJ/mol)
evident between all atoms, including inert
gases and especially between covalently
bonded molecules.
Bonds are created through both atomic and
molecular dipoles
Secondary Bonding
Hydrogen bonding
special type of secondary bond between
molecules with permenant dipoles and
hydrogen in the compound.
Ex: HF, H2O, NH3
these secondary bonds can have strengths as
high as ~50 kJ/mol and will cause increases
in melting temperature above those normally
expected.
Metallic Bonding
Most common in bonding of metals and
their alloys.
Proposed model of metallic bonding
metals usually have, at most, 3 valence
electrons, all of which form an “electron sea”,
which drift through the entire metal.
Base electrons form net-positive ion cores,
which attract the free electrons from the
“sea” as needed to maintain neutrality.
Metallic Bonding
Bonding may be weak or strong,
depending upon atoms involved.
Ex: Hg bonding energy = 68 kJ/mol
W bonding energy = 850 kJ/mol
Metallic Bonding
Potentials for metallic bonding are most
commonly calculated via the EAM,
especially in alloys and intermetallics
Link to Paper by Dr. Farkas